AIC.gkwreg: Akaike Information Criterion for GKw Regression Models

In gkwreg: Generalized Kumaraswamy Regression Models for Bounded Data

Akaike Information Criterion for GKw Regression Models

Description

Calculates the Akaike Information Criterion (AIC) for fitted Generalized Kumaraswamy regression models.

Usage

## S3 method for class 'gkwreg'
AIC(object, ..., k = 2)

Arguments

object	An object of class "gkwreg", typically obtained from gkwreg.
...	Optionally more fitted model objects.
k	Numeric, the penalty per parameter. Default is k = 2 for classical AIC. Setting k = log(n) gives BIC-equivalent penalty.

Details

The AIC is computed as:

AIC = -2\ell(\hat{\theta}) + k \cdot p

where \ell(\hat{\theta}) is the maximized log-likelihood and p is the number of estimated parameters.

When multiple objects are provided, a data frame comparing all models is returned. Lower AIC values indicate better models, balancing goodness-of-fit against model complexity.

For small sample sizes, consider the corrected AIC (AICc):

AICc = AIC + \frac{2p(p+1)}{n-p-1}

where n is the sample size. This correction is not automatically applied but can be calculated manually.

Value

If only one object is provided, returns a numeric value with the AIC. If multiple objects are provided, returns a data frame with columns df and AIC, with rows named according to the object names in the call.

Author(s)

Lopes, J. E.

References

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1109/TAC.1974.1100705")}

Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research, 33(2), 261–304. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0049124104268644")}

See Also

gkwreg, logLik.gkwreg, BIC.gkwreg

Examples

# Load example data
data(GasolineYield)

# Fit competing models
fit1 <- gkwreg(yield ~ batch, data = GasolineYield, family = "kw")
fit2 <- gkwreg(yield ~ batch + temp, data = GasolineYield, family = "kw")
fit3 <- gkwreg(yield ~ temp, data = GasolineYield, family = "kw")

# Calculate AIC for single model
AIC(fit1)

# Compare multiple models (with proper names)
AIC(fit1, fit2, fit3)

# Use different penalty
AIC(fit1, k = 4)

gkwreg documentation built on Nov. 27, 2025, 5:06 p.m.